The "Discussion" section on that WP article describes the flaw in the experiment. These calculations could probably be reproduced by the people you listed.
After some head scratching I came up with a differential equation describing the motion of the torsion balance arm. Assuming there is no torque from the suspending string, no atmosphere, and a massless arm, the dynamics are:
d²θ GM ( cos θ/2 sin θ/2 )
---- = ----- ( -------------- - ---------------- )
dt² 2R³ ( 1 - cos θ/2 1 + cos θ/2 )
where G is the gravitational constant, M is the mass of each fixed weight, and 2R is the distance along the balance arm at which the smaller masses are placed.
I couldn't find an analytical solution to this equation, but a numerical simulation showed that, starting from an angle of θ=10°, it took just over ten minutes for the arm to complete its motion (I used values of M and R from the website).
I am running the simulation on a greater variety of initial states, and report results when I have them. For now, however, it would appear that it is entirely possible that Bending Spacetime in the Basement could be a genuine demonstration of gravitational attraction between two small objects.